Question

Various studies indicate that approximately 8% of the world's population is left-handed. You think this number is actually higher. You take an SRS of 230 people and find that 30 of them are left-handed. Test your claim at the 5% significance level.

a. State your null and alternative hypotheses.

b.State the rejection region.

c. Calculate the test statistic.

d. Determine the P-value for your test.

e. State your conclusion for your hypothesis test.

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.08

Ha : p > 0.8

= x / n = 30/230 = 0.1304

P0 = 0.08

1 - P0 = 1 -0.08 = 0.92

= 0.05

The critical value = 1.645

z < 1.645

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.1304 - 0.08 / [0.08*(0.92) /230 ]

= 2.817

P(z >2.817 ) = 1 - P(z <2.817 ) = 0.0024

P-value = 0.0024

= 0.05

0.0024< 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that